1//! Constants for the `f32` single-precision floating point type.
2//!
3//! *[See also the `f32` primitive type][f32].*
4//!
5//! Mathematically significant numbers are provided in the `consts` sub-module.
6//!
7//! For the constants defined directly in this module
8//! (as distinct from those defined in the `consts` sub-module),
9//! new code should instead use the associated constants
10//! defined directly on the `f32` type.
11
12#![stable(feature = "rust1", since = "1.0.0")]
13
14use crate::convert::FloatToInt;
15use crate::num::FpCategory;
16use crate::panic::const_assert;
17use crate::{cfg_select, intrinsics, mem};
18
19/// The radix or base of the internal representation of `f32`.
20/// Use [`f32::RADIX`] instead.
21///
22/// # Examples
23///
24/// ```rust
25/// // deprecated way
26/// # #[allow(deprecated, deprecated_in_future)]
27/// let r = std::f32::RADIX;
28///
29/// // intended way
30/// let r = f32::RADIX;
31/// ```
32#[stable(feature = "rust1", since = "1.0.0")]
33#[deprecated(since = "TBD", note = "replaced by the `RADIX` associated constant on `f32`")]
34#[rustc_diagnostic_item = "f32_legacy_const_radix"]
35pub const RADIX: u32 = f32::RADIX;
36
37/// Number of significant digits in base 2.
38/// Use [`f32::MANTISSA_DIGITS`] instead.
39///
40/// # Examples
41///
42/// ```rust
43/// // deprecated way
44/// # #[allow(deprecated, deprecated_in_future)]
45/// let d = std::f32::MANTISSA_DIGITS;
46///
47/// // intended way
48/// let d = f32::MANTISSA_DIGITS;
49/// ```
50#[stable(feature = "rust1", since = "1.0.0")]
51#[deprecated(
52 since = "TBD",
53 note = "replaced by the `MANTISSA_DIGITS` associated constant on `f32`"
54)]
55#[rustc_diagnostic_item = "f32_legacy_const_mantissa_dig"]
56pub const MANTISSA_DIGITS: u32 = f32::MANTISSA_DIGITS;
57
58/// Approximate number of significant digits in base 10.
59/// Use [`f32::DIGITS`] instead.
60///
61/// # Examples
62///
63/// ```rust
64/// // deprecated way
65/// # #[allow(deprecated, deprecated_in_future)]
66/// let d = std::f32::DIGITS;
67///
68/// // intended way
69/// let d = f32::DIGITS;
70/// ```
71#[stable(feature = "rust1", since = "1.0.0")]
72#[deprecated(since = "TBD", note = "replaced by the `DIGITS` associated constant on `f32`")]
73#[rustc_diagnostic_item = "f32_legacy_const_digits"]
74pub const DIGITS: u32 = f32::DIGITS;
75
76/// [Machine epsilon] value for `f32`.
77/// Use [`f32::EPSILON`] instead.
78///
79/// This is the difference between `1.0` and the next larger representable number.
80///
81/// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
82///
83/// # Examples
84///
85/// ```rust
86/// // deprecated way
87/// # #[allow(deprecated, deprecated_in_future)]
88/// let e = std::f32::EPSILON;
89///
90/// // intended way
91/// let e = f32::EPSILON;
92/// ```
93#[stable(feature = "rust1", since = "1.0.0")]
94#[deprecated(since = "TBD", note = "replaced by the `EPSILON` associated constant on `f32`")]
95#[rustc_diagnostic_item = "f32_legacy_const_epsilon"]
96pub const EPSILON: f32 = f32::EPSILON;
97
98/// Smallest finite `f32` value.
99/// Use [`f32::MIN`] instead.
100///
101/// # Examples
102///
103/// ```rust
104/// // deprecated way
105/// # #[allow(deprecated, deprecated_in_future)]
106/// let min = std::f32::MIN;
107///
108/// // intended way
109/// let min = f32::MIN;
110/// ```
111#[stable(feature = "rust1", since = "1.0.0")]
112#[deprecated(since = "TBD", note = "replaced by the `MIN` associated constant on `f32`")]
113#[rustc_diagnostic_item = "f32_legacy_const_min"]
114pub const MIN: f32 = f32::MIN;
115
116/// Smallest positive normal `f32` value.
117/// Use [`f32::MIN_POSITIVE`] instead.
118///
119/// # Examples
120///
121/// ```rust
122/// // deprecated way
123/// # #[allow(deprecated, deprecated_in_future)]
124/// let min = std::f32::MIN_POSITIVE;
125///
126/// // intended way
127/// let min = f32::MIN_POSITIVE;
128/// ```
129#[stable(feature = "rust1", since = "1.0.0")]
130#[deprecated(since = "TBD", note = "replaced by the `MIN_POSITIVE` associated constant on `f32`")]
131#[rustc_diagnostic_item = "f32_legacy_const_min_positive"]
132pub const MIN_POSITIVE: f32 = f32::MIN_POSITIVE;
133
134/// Largest finite `f32` value.
135/// Use [`f32::MAX`] instead.
136///
137/// # Examples
138///
139/// ```rust
140/// // deprecated way
141/// # #[allow(deprecated, deprecated_in_future)]
142/// let max = std::f32::MAX;
143///
144/// // intended way
145/// let max = f32::MAX;
146/// ```
147#[stable(feature = "rust1", since = "1.0.0")]
148#[deprecated(since = "TBD", note = "replaced by the `MAX` associated constant on `f32`")]
149#[rustc_diagnostic_item = "f32_legacy_const_max"]
150pub const MAX: f32 = f32::MAX;
151
152/// One greater than the minimum possible normal power of 2 exponent.
153/// Use [`f32::MIN_EXP`] instead.
154///
155/// # Examples
156///
157/// ```rust
158/// // deprecated way
159/// # #[allow(deprecated, deprecated_in_future)]
160/// let min = std::f32::MIN_EXP;
161///
162/// // intended way
163/// let min = f32::MIN_EXP;
164/// ```
165#[stable(feature = "rust1", since = "1.0.0")]
166#[deprecated(since = "TBD", note = "replaced by the `MIN_EXP` associated constant on `f32`")]
167#[rustc_diagnostic_item = "f32_legacy_const_min_exp"]
168pub const MIN_EXP: i32 = f32::MIN_EXP;
169
170/// Maximum possible power of 2 exponent.
171/// Use [`f32::MAX_EXP`] instead.
172///
173/// # Examples
174///
175/// ```rust
176/// // deprecated way
177/// # #[allow(deprecated, deprecated_in_future)]
178/// let max = std::f32::MAX_EXP;
179///
180/// // intended way
181/// let max = f32::MAX_EXP;
182/// ```
183#[stable(feature = "rust1", since = "1.0.0")]
184#[deprecated(since = "TBD", note = "replaced by the `MAX_EXP` associated constant on `f32`")]
185#[rustc_diagnostic_item = "f32_legacy_const_max_exp"]
186pub const MAX_EXP: i32 = f32::MAX_EXP;
187
188/// Minimum possible normal power of 10 exponent.
189/// Use [`f32::MIN_10_EXP`] instead.
190///
191/// # Examples
192///
193/// ```rust
194/// // deprecated way
195/// # #[allow(deprecated, deprecated_in_future)]
196/// let min = std::f32::MIN_10_EXP;
197///
198/// // intended way
199/// let min = f32::MIN_10_EXP;
200/// ```
201#[stable(feature = "rust1", since = "1.0.0")]
202#[deprecated(since = "TBD", note = "replaced by the `MIN_10_EXP` associated constant on `f32`")]
203#[rustc_diagnostic_item = "f32_legacy_const_min_10_exp"]
204pub const MIN_10_EXP: i32 = f32::MIN_10_EXP;
205
206/// Maximum possible power of 10 exponent.
207/// Use [`f32::MAX_10_EXP`] instead.
208///
209/// # Examples
210///
211/// ```rust
212/// // deprecated way
213/// # #[allow(deprecated, deprecated_in_future)]
214/// let max = std::f32::MAX_10_EXP;
215///
216/// // intended way
217/// let max = f32::MAX_10_EXP;
218/// ```
219#[stable(feature = "rust1", since = "1.0.0")]
220#[deprecated(since = "TBD", note = "replaced by the `MAX_10_EXP` associated constant on `f32`")]
221#[rustc_diagnostic_item = "f32_legacy_const_max_10_exp"]
222pub const MAX_10_EXP: i32 = f32::MAX_10_EXP;
223
224/// Not a Number (NaN).
225/// Use [`f32::NAN`] instead.
226///
227/// # Examples
228///
229/// ```rust
230/// // deprecated way
231/// # #[allow(deprecated, deprecated_in_future)]
232/// let nan = std::f32::NAN;
233///
234/// // intended way
235/// let nan = f32::NAN;
236/// ```
237#[stable(feature = "rust1", since = "1.0.0")]
238#[deprecated(since = "TBD", note = "replaced by the `NAN` associated constant on `f32`")]
239#[rustc_diagnostic_item = "f32_legacy_const_nan"]
240pub const NAN: f32 = f32::NAN;
241
242/// Infinity (∞).
243/// Use [`f32::INFINITY`] instead.
244///
245/// # Examples
246///
247/// ```rust
248/// // deprecated way
249/// # #[allow(deprecated, deprecated_in_future)]
250/// let inf = std::f32::INFINITY;
251///
252/// // intended way
253/// let inf = f32::INFINITY;
254/// ```
255#[stable(feature = "rust1", since = "1.0.0")]
256#[deprecated(since = "TBD", note = "replaced by the `INFINITY` associated constant on `f32`")]
257#[rustc_diagnostic_item = "f32_legacy_const_infinity"]
258pub const INFINITY: f32 = f32::INFINITY;
259
260/// Negative infinity (−∞).
261/// Use [`f32::NEG_INFINITY`] instead.
262///
263/// # Examples
264///
265/// ```rust
266/// // deprecated way
267/// # #[allow(deprecated, deprecated_in_future)]
268/// let ninf = std::f32::NEG_INFINITY;
269///
270/// // intended way
271/// let ninf = f32::NEG_INFINITY;
272/// ```
273#[stable(feature = "rust1", since = "1.0.0")]
274#[deprecated(since = "TBD", note = "replaced by the `NEG_INFINITY` associated constant on `f32`")]
275#[rustc_diagnostic_item = "f32_legacy_const_neg_infinity"]
276pub const NEG_INFINITY: f32 = f32::NEG_INFINITY;
277
278/// Basic mathematical constants.
279#[stable(feature = "rust1", since = "1.0.0")]
280pub mod consts {
281 // FIXME: replace with mathematical constants from cmath.
282
283 /// Archimedes' constant (π)
284 #[stable(feature = "rust1", since = "1.0.0")]
285 pub const PI: f32 = 3.14159265358979323846264338327950288_f32;
286
287 /// The full circle constant (τ)
288 ///
289 /// Equal to 2π.
290 #[stable(feature = "tau_constant", since = "1.47.0")]
291 pub const TAU: f32 = 6.28318530717958647692528676655900577_f32;
292
293 /// The golden ratio (φ)
294 #[unstable(feature = "more_float_constants", issue = "103883")]
295 pub const PHI: f32 = 1.618033988749894848204586834365638118_f32;
296
297 /// The Euler-Mascheroni constant (γ)
298 #[unstable(feature = "more_float_constants", issue = "103883")]
299 pub const EGAMMA: f32 = 0.577215664901532860606512090082402431_f32;
300
301 /// π/2
302 #[stable(feature = "rust1", since = "1.0.0")]
303 pub const FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
304
305 /// π/3
306 #[stable(feature = "rust1", since = "1.0.0")]
307 pub const FRAC_PI_3: f32 = 1.04719755119659774615421446109316763_f32;
308
309 /// π/4
310 #[stable(feature = "rust1", since = "1.0.0")]
311 pub const FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;
312
313 /// π/6
314 #[stable(feature = "rust1", since = "1.0.0")]
315 pub const FRAC_PI_6: f32 = 0.52359877559829887307710723054658381_f32;
316
317 /// π/8
318 #[stable(feature = "rust1", since = "1.0.0")]
319 pub const FRAC_PI_8: f32 = 0.39269908169872415480783042290993786_f32;
320
321 /// 1/π
322 #[stable(feature = "rust1", since = "1.0.0")]
323 pub const FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;
324
325 /// 1/sqrt(π)
326 #[unstable(feature = "more_float_constants", issue = "103883")]
327 pub const FRAC_1_SQRT_PI: f32 = 0.564189583547756286948079451560772586_f32;
328
329 /// 1/sqrt(2π)
330 #[doc(alias = "FRAC_1_SQRT_TAU")]
331 #[unstable(feature = "more_float_constants", issue = "103883")]
332 pub const FRAC_1_SQRT_2PI: f32 = 0.398942280401432677939946059934381868_f32;
333
334 /// 2/π
335 #[stable(feature = "rust1", since = "1.0.0")]
336 pub const FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;
337
338 /// 2/sqrt(π)
339 #[stable(feature = "rust1", since = "1.0.0")]
340 pub const FRAC_2_SQRT_PI: f32 = 1.12837916709551257389615890312154517_f32;
341
342 /// sqrt(2)
343 #[stable(feature = "rust1", since = "1.0.0")]
344 pub const SQRT_2: f32 = 1.41421356237309504880168872420969808_f32;
345
346 /// 1/sqrt(2)
347 #[stable(feature = "rust1", since = "1.0.0")]
348 pub const FRAC_1_SQRT_2: f32 = 0.707106781186547524400844362104849039_f32;
349
350 /// sqrt(3)
351 #[unstable(feature = "more_float_constants", issue = "103883")]
352 pub const SQRT_3: f32 = 1.732050807568877293527446341505872367_f32;
353
354 /// 1/sqrt(3)
355 #[unstable(feature = "more_float_constants", issue = "103883")]
356 pub const FRAC_1_SQRT_3: f32 = 0.577350269189625764509148780501957456_f32;
357
358 /// Euler's number (e)
359 #[stable(feature = "rust1", since = "1.0.0")]
360 pub const E: f32 = 2.71828182845904523536028747135266250_f32;
361
362 /// log<sub>2</sub>(e)
363 #[stable(feature = "rust1", since = "1.0.0")]
364 pub const LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
365
366 /// log<sub>2</sub>(10)
367 #[stable(feature = "extra_log_consts", since = "1.43.0")]
368 pub const LOG2_10: f32 = 3.32192809488736234787031942948939018_f32;
369
370 /// log<sub>10</sub>(e)
371 #[stable(feature = "rust1", since = "1.0.0")]
372 pub const LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
373
374 /// log<sub>10</sub>(2)
375 #[stable(feature = "extra_log_consts", since = "1.43.0")]
376 pub const LOG10_2: f32 = 0.301029995663981195213738894724493027_f32;
377
378 /// ln(2)
379 #[stable(feature = "rust1", since = "1.0.0")]
380 pub const LN_2: f32 = 0.693147180559945309417232121458176568_f32;
381
382 /// ln(10)
383 #[stable(feature = "rust1", since = "1.0.0")]
384 pub const LN_10: f32 = 2.30258509299404568401799145468436421_f32;
385}
386
387impl f32 {
388 /// The radix or base of the internal representation of `f32`.
389 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
390 pub const RADIX: u32 = 2;
391
392 /// Number of significant digits in base 2.
393 ///
394 /// Note that the size of the mantissa in the bitwise representation is one
395 /// smaller than this since the leading 1 is not stored explicitly.
396 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
397 pub const MANTISSA_DIGITS: u32 = 24;
398
399 /// Approximate number of significant digits in base 10.
400 ///
401 /// This is the maximum <i>x</i> such that any decimal number with <i>x</i>
402 /// significant digits can be converted to `f32` and back without loss.
403 ///
404 /// Equal to floor(log<sub>10</sub>&nbsp;2<sup>[`MANTISSA_DIGITS`]&nbsp;&minus;&nbsp;1</sup>).
405 ///
406 /// [`MANTISSA_DIGITS`]: f32::MANTISSA_DIGITS
407 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
408 pub const DIGITS: u32 = 6;
409
410 /// [Machine epsilon] value for `f32`.
411 ///
412 /// This is the difference between `1.0` and the next larger representable number.
413 ///
414 /// Equal to 2<sup>1&nbsp;&minus;&nbsp;[`MANTISSA_DIGITS`]</sup>.
415 ///
416 /// [Machine epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
417 /// [`MANTISSA_DIGITS`]: f32::MANTISSA_DIGITS
418 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
419 #[rustc_diagnostic_item = "f32_epsilon"]
420 pub const EPSILON: f32 = 1.19209290e-07_f32;
421
422 /// Smallest finite `f32` value.
423 ///
424 /// Equal to &minus;[`MAX`].
425 ///
426 /// [`MAX`]: f32::MAX
427 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
428 pub const MIN: f32 = -3.40282347e+38_f32;
429 /// Smallest positive normal `f32` value.
430 ///
431 /// Equal to 2<sup>[`MIN_EXP`]&nbsp;&minus;&nbsp;1</sup>.
432 ///
433 /// [`MIN_EXP`]: f32::MIN_EXP
434 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
435 pub const MIN_POSITIVE: f32 = 1.17549435e-38_f32;
436 /// Largest finite `f32` value.
437 ///
438 /// Equal to
439 /// (1&nbsp;&minus;&nbsp;2<sup>&minus;[`MANTISSA_DIGITS`]</sup>)&nbsp;2<sup>[`MAX_EXP`]</sup>.
440 ///
441 /// [`MANTISSA_DIGITS`]: f32::MANTISSA_DIGITS
442 /// [`MAX_EXP`]: f32::MAX_EXP
443 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
444 pub const MAX: f32 = 3.40282347e+38_f32;
445
446 /// One greater than the minimum possible *normal* power of 2 exponent
447 /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
448 ///
449 /// This corresponds to the exact minimum possible *normal* power of 2 exponent
450 /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
451 /// In other words, all normal numbers representable by this type are
452 /// greater than or equal to 0.5&nbsp;×&nbsp;2<sup><i>MIN_EXP</i></sup>.
453 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
454 pub const MIN_EXP: i32 = -125;
455 /// One greater than the maximum possible power of 2 exponent
456 /// for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).
457 ///
458 /// This corresponds to the exact maximum possible power of 2 exponent
459 /// for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition).
460 /// In other words, all numbers representable by this type are
461 /// strictly less than 2<sup><i>MAX_EXP</i></sup>.
462 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
463 pub const MAX_EXP: i32 = 128;
464
465 /// Minimum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
466 ///
467 /// Equal to ceil(log<sub>10</sub>&nbsp;[`MIN_POSITIVE`]).
468 ///
469 /// [`MIN_POSITIVE`]: f32::MIN_POSITIVE
470 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
471 pub const MIN_10_EXP: i32 = -37;
472 /// Maximum <i>x</i> for which 10<sup><i>x</i></sup> is normal.
473 ///
474 /// Equal to floor(log<sub>10</sub>&nbsp;[`MAX`]).
475 ///
476 /// [`MAX`]: f32::MAX
477 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
478 pub const MAX_10_EXP: i32 = 38;
479
480 /// Not a Number (NaN).
481 ///
482 /// Note that IEEE 754 doesn't define just a single NaN value; a plethora of bit patterns are
483 /// considered to be NaN. Furthermore, the standard makes a difference between a "signaling" and
484 /// a "quiet" NaN, and allows inspecting its "payload" (the unspecified bits in the bit pattern)
485 /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
486 /// info.
487 ///
488 /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
489 /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
490 /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
491 /// The concrete bit pattern may change across Rust versions and target platforms.
492 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
493 #[rustc_diagnostic_item = "f32_nan"]
494 #[allow(clippy::eq_op)]
495 pub const NAN: f32 = 0.0_f32 / 0.0_f32;
496 /// Infinity (∞).
497 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
498 pub const INFINITY: f32 = 1.0_f32 / 0.0_f32;
499 /// Negative infinity (−∞).
500 #[stable(feature = "assoc_int_consts", since = "1.43.0")]
501 pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32;
502
503 /// Sign bit
504 pub(crate) const SIGN_MASK: u32 = 0x8000_0000;
505
506 /// Exponent mask
507 pub(crate) const EXP_MASK: u32 = 0x7f80_0000;
508
509 /// Mantissa mask
510 pub(crate) const MAN_MASK: u32 = 0x007f_ffff;
511
512 /// Minimum representable positive value (min subnormal)
513 const TINY_BITS: u32 = 0x1;
514
515 /// Minimum representable negative value (min negative subnormal)
516 const NEG_TINY_BITS: u32 = Self::TINY_BITS | Self::SIGN_MASK;
517
518 /// Returns `true` if this value is NaN.
519 ///
520 /// ```
521 /// let nan = f32::NAN;
522 /// let f = 7.0_f32;
523 ///
524 /// assert!(nan.is_nan());
525 /// assert!(!f.is_nan());
526 /// ```
527 #[must_use]
528 #[stable(feature = "rust1", since = "1.0.0")]
529 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
530 #[inline]
531 #[allow(clippy::eq_op)] // > if you intended to check if the operand is NaN, use `.is_nan()` instead :)
532 pub const fn is_nan(self) -> bool {
533 self != self
534 }
535
536 /// Returns `true` if this value is positive infinity or negative infinity, and
537 /// `false` otherwise.
538 ///
539 /// ```
540 /// let f = 7.0f32;
541 /// let inf = f32::INFINITY;
542 /// let neg_inf = f32::NEG_INFINITY;
543 /// let nan = f32::NAN;
544 ///
545 /// assert!(!f.is_infinite());
546 /// assert!(!nan.is_infinite());
547 ///
548 /// assert!(inf.is_infinite());
549 /// assert!(neg_inf.is_infinite());
550 /// ```
551 #[must_use]
552 #[stable(feature = "rust1", since = "1.0.0")]
553 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
554 #[inline]
555 pub const fn is_infinite(self) -> bool {
556 // Getting clever with transmutation can result in incorrect answers on some FPUs
557 // FIXME: alter the Rust <-> Rust calling convention to prevent this problem.
558 // See https://github.com/rust-lang/rust/issues/72327
559 (self == f32::INFINITY) | (self == f32::NEG_INFINITY)
560 }
561
562 /// Returns `true` if this number is neither infinite nor NaN.
563 ///
564 /// ```
565 /// let f = 7.0f32;
566 /// let inf = f32::INFINITY;
567 /// let neg_inf = f32::NEG_INFINITY;
568 /// let nan = f32::NAN;
569 ///
570 /// assert!(f.is_finite());
571 ///
572 /// assert!(!nan.is_finite());
573 /// assert!(!inf.is_finite());
574 /// assert!(!neg_inf.is_finite());
575 /// ```
576 #[must_use]
577 #[stable(feature = "rust1", since = "1.0.0")]
578 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
579 #[inline]
580 pub const fn is_finite(self) -> bool {
581 // There's no need to handle NaN separately: if self is NaN,
582 // the comparison is not true, exactly as desired.
583 self.abs() < Self::INFINITY
584 }
585
586 /// Returns `true` if the number is [subnormal].
587 ///
588 /// ```
589 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
590 /// let max = f32::MAX;
591 /// let lower_than_min = 1.0e-40_f32;
592 /// let zero = 0.0_f32;
593 ///
594 /// assert!(!min.is_subnormal());
595 /// assert!(!max.is_subnormal());
596 ///
597 /// assert!(!zero.is_subnormal());
598 /// assert!(!f32::NAN.is_subnormal());
599 /// assert!(!f32::INFINITY.is_subnormal());
600 /// // Values between `0` and `min` are Subnormal.
601 /// assert!(lower_than_min.is_subnormal());
602 /// ```
603 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
604 #[must_use]
605 #[stable(feature = "is_subnormal", since = "1.53.0")]
606 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
607 #[inline]
608 pub const fn is_subnormal(self) -> bool {
609 matches!(self.classify(), FpCategory::Subnormal)
610 }
611
612 /// Returns `true` if the number is neither zero, infinite,
613 /// [subnormal], or NaN.
614 ///
615 /// ```
616 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
617 /// let max = f32::MAX;
618 /// let lower_than_min = 1.0e-40_f32;
619 /// let zero = 0.0_f32;
620 ///
621 /// assert!(min.is_normal());
622 /// assert!(max.is_normal());
623 ///
624 /// assert!(!zero.is_normal());
625 /// assert!(!f32::NAN.is_normal());
626 /// assert!(!f32::INFINITY.is_normal());
627 /// // Values between `0` and `min` are Subnormal.
628 /// assert!(!lower_than_min.is_normal());
629 /// ```
630 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
631 #[must_use]
632 #[stable(feature = "rust1", since = "1.0.0")]
633 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
634 #[inline]
635 pub const fn is_normal(self) -> bool {
636 matches!(self.classify(), FpCategory::Normal)
637 }
638
639 /// Returns the floating point category of the number. If only one property
640 /// is going to be tested, it is generally faster to use the specific
641 /// predicate instead.
642 ///
643 /// ```
644 /// use std::num::FpCategory;
645 ///
646 /// let num = 12.4_f32;
647 /// let inf = f32::INFINITY;
648 ///
649 /// assert_eq!(num.classify(), FpCategory::Normal);
650 /// assert_eq!(inf.classify(), FpCategory::Infinite);
651 /// ```
652 #[stable(feature = "rust1", since = "1.0.0")]
653 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
654 pub const fn classify(self) -> FpCategory {
655 // We used to have complicated logic here that avoids the simple bit-based tests to work
656 // around buggy codegen for x87 targets (see
657 // https://github.com/rust-lang/rust/issues/114479). However, some LLVM versions later, none
658 // of our tests is able to find any difference between the complicated and the naive
659 // version, so now we are back to the naive version.
660 let b = self.to_bits();
661 match (b & Self::MAN_MASK, b & Self::EXP_MASK) {
662 (0, Self::EXP_MASK) => FpCategory::Infinite,
663 (_, Self::EXP_MASK) => FpCategory::Nan,
664 (0, 0) => FpCategory::Zero,
665 (_, 0) => FpCategory::Subnormal,
666 _ => FpCategory::Normal,
667 }
668 }
669
670 /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
671 /// positive sign bit and positive infinity.
672 ///
673 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
674 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
675 /// conserved over arithmetic operations, the result of `is_sign_positive` on
676 /// a NaN might produce an unexpected or non-portable result. See the [specification
677 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == 1.0`
678 /// if you need fully portable behavior (will return `false` for all NaNs).
679 ///
680 /// ```
681 /// let f = 7.0_f32;
682 /// let g = -7.0_f32;
683 ///
684 /// assert!(f.is_sign_positive());
685 /// assert!(!g.is_sign_positive());
686 /// ```
687 #[must_use]
688 #[stable(feature = "rust1", since = "1.0.0")]
689 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
690 #[inline]
691 pub const fn is_sign_positive(self) -> bool {
692 !self.is_sign_negative()
693 }
694
695 /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
696 /// negative sign bit and negative infinity.
697 ///
698 /// Note that IEEE 754 doesn't assign any meaning to the sign bit in case of
699 /// a NaN, and as Rust doesn't guarantee that the bit pattern of NaNs are
700 /// conserved over arithmetic operations, the result of `is_sign_negative` on
701 /// a NaN might produce an unexpected or non-portable result. See the [specification
702 /// of NaN bit patterns](f32#nan-bit-patterns) for more info. Use `self.signum() == -1.0`
703 /// if you need fully portable behavior (will return `false` for all NaNs).
704 ///
705 /// ```
706 /// let f = 7.0f32;
707 /// let g = -7.0f32;
708 ///
709 /// assert!(!f.is_sign_negative());
710 /// assert!(g.is_sign_negative());
711 /// ```
712 #[must_use]
713 #[stable(feature = "rust1", since = "1.0.0")]
714 #[rustc_const_stable(feature = "const_float_classify", since = "1.83.0")]
715 #[inline]
716 pub const fn is_sign_negative(self) -> bool {
717 // IEEE754 says: isSignMinus(x) is true if and only if x has negative sign. isSignMinus
718 // applies to zeros and NaNs as well.
719 self.to_bits() & 0x8000_0000 != 0
720 }
721
722 /// Returns the least number greater than `self`.
723 ///
724 /// Let `TINY` be the smallest representable positive `f32`. Then,
725 /// - if `self.is_nan()`, this returns `self`;
726 /// - if `self` is [`NEG_INFINITY`], this returns [`MIN`];
727 /// - if `self` is `-TINY`, this returns -0.0;
728 /// - if `self` is -0.0 or +0.0, this returns `TINY`;
729 /// - if `self` is [`MAX`] or [`INFINITY`], this returns [`INFINITY`];
730 /// - otherwise the unique least value greater than `self` is returned.
731 ///
732 /// The identity `x.next_up() == -(-x).next_down()` holds for all non-NaN `x`. When `x`
733 /// is finite `x == x.next_up().next_down()` also holds.
734 ///
735 /// ```rust
736 /// // f32::EPSILON is the difference between 1.0 and the next number up.
737 /// assert_eq!(1.0f32.next_up(), 1.0 + f32::EPSILON);
738 /// // But not for most numbers.
739 /// assert!(0.1f32.next_up() < 0.1 + f32::EPSILON);
740 /// assert_eq!(16777216f32.next_up(), 16777218.0);
741 /// ```
742 ///
743 /// This operation corresponds to IEEE-754 `nextUp`.
744 ///
745 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
746 /// [`INFINITY`]: Self::INFINITY
747 /// [`MIN`]: Self::MIN
748 /// [`MAX`]: Self::MAX
749 #[inline]
750 #[doc(alias = "nextUp")]
751 #[stable(feature = "float_next_up_down", since = "1.86.0")]
752 #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
753 pub const fn next_up(self) -> Self {
754 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
755 // denormals to zero. This is in general unsound and unsupported, but here
756 // we do our best to still produce the correct result on such targets.
757 let bits = self.to_bits();
758 if self.is_nan() || bits == Self::INFINITY.to_bits() {
759 return self;
760 }
761
762 let abs = bits & !Self::SIGN_MASK;
763 let next_bits = if abs == 0 {
764 Self::TINY_BITS
765 } else if bits == abs {
766 bits + 1
767 } else {
768 bits - 1
769 };
770 Self::from_bits(next_bits)
771 }
772
773 /// Returns the greatest number less than `self`.
774 ///
775 /// Let `TINY` be the smallest representable positive `f32`. Then,
776 /// - if `self.is_nan()`, this returns `self`;
777 /// - if `self` is [`INFINITY`], this returns [`MAX`];
778 /// - if `self` is `TINY`, this returns 0.0;
779 /// - if `self` is -0.0 or +0.0, this returns `-TINY`;
780 /// - if `self` is [`MIN`] or [`NEG_INFINITY`], this returns [`NEG_INFINITY`];
781 /// - otherwise the unique greatest value less than `self` is returned.
782 ///
783 /// The identity `x.next_down() == -(-x).next_up()` holds for all non-NaN `x`. When `x`
784 /// is finite `x == x.next_down().next_up()` also holds.
785 ///
786 /// ```rust
787 /// let x = 1.0f32;
788 /// // Clamp value into range [0, 1).
789 /// let clamped = x.clamp(0.0, 1.0f32.next_down());
790 /// assert!(clamped < 1.0);
791 /// assert_eq!(clamped.next_up(), 1.0);
792 /// ```
793 ///
794 /// This operation corresponds to IEEE-754 `nextDown`.
795 ///
796 /// [`NEG_INFINITY`]: Self::NEG_INFINITY
797 /// [`INFINITY`]: Self::INFINITY
798 /// [`MIN`]: Self::MIN
799 /// [`MAX`]: Self::MAX
800 #[inline]
801 #[doc(alias = "nextDown")]
802 #[stable(feature = "float_next_up_down", since = "1.86.0")]
803 #[rustc_const_stable(feature = "float_next_up_down", since = "1.86.0")]
804 pub const fn next_down(self) -> Self {
805 // Some targets violate Rust's assumption of IEEE semantics, e.g. by flushing
806 // denormals to zero. This is in general unsound and unsupported, but here
807 // we do our best to still produce the correct result on such targets.
808 let bits = self.to_bits();
809 if self.is_nan() || bits == Self::NEG_INFINITY.to_bits() {
810 return self;
811 }
812
813 let abs = bits & !Self::SIGN_MASK;
814 let next_bits = if abs == 0 {
815 Self::NEG_TINY_BITS
816 } else if bits == abs {
817 bits - 1
818 } else {
819 bits + 1
820 };
821 Self::from_bits(next_bits)
822 }
823
824 /// Takes the reciprocal (inverse) of a number, `1/x`.
825 ///
826 /// ```
827 /// let x = 2.0_f32;
828 /// let abs_difference = (x.recip() - (1.0 / x)).abs();
829 ///
830 /// assert!(abs_difference <= f32::EPSILON);
831 /// ```
832 #[must_use = "this returns the result of the operation, without modifying the original"]
833 #[stable(feature = "rust1", since = "1.0.0")]
834 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
835 #[inline]
836 pub const fn recip(self) -> f32 {
837 1.0 / self
838 }
839
840 /// Converts radians to degrees.
841 ///
842 /// ```
843 /// let angle = std::f32::consts::PI;
844 ///
845 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
846 /// # #[cfg(any(not(target_arch = "x86"), target_feature = "sse2"))]
847 /// assert!(abs_difference <= f32::EPSILON);
848 /// ```
849 #[must_use = "this returns the result of the operation, \
850 without modifying the original"]
851 #[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
852 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
853 #[inline]
854 pub const fn to_degrees(self) -> f32 {
855 // Use a constant for better precision.
856 const PIS_IN_180: f32 = 57.2957795130823208767981548141051703_f32;
857 self * PIS_IN_180
858 }
859
860 /// Converts degrees to radians.
861 ///
862 /// ```
863 /// let angle = 180.0f32;
864 ///
865 /// let abs_difference = (angle.to_radians() - std::f32::consts::PI).abs();
866 ///
867 /// assert!(abs_difference <= f32::EPSILON);
868 /// ```
869 #[must_use = "this returns the result of the operation, \
870 without modifying the original"]
871 #[stable(feature = "f32_deg_rad_conversions", since = "1.7.0")]
872 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
873 #[inline]
874 pub const fn to_radians(self) -> f32 {
875 const RADS_PER_DEG: f32 = consts::PI / 180.0;
876 self * RADS_PER_DEG
877 }
878
879 /// Returns the maximum of the two numbers, ignoring NaN.
880 ///
881 /// If one of the arguments is NaN, then the other argument is returned.
882 /// This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs;
883 /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
884 /// This also matches the behavior of libm’s fmax. In particular, if the inputs compare equal
885 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
886 ///
887 /// ```
888 /// let x = 1.0f32;
889 /// let y = 2.0f32;
890 ///
891 /// assert_eq!(x.max(y), y);
892 /// ```
893 #[must_use = "this returns the result of the comparison, without modifying either input"]
894 #[stable(feature = "rust1", since = "1.0.0")]
895 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
896 #[inline]
897 pub const fn max(self, other: f32) -> f32 {
898 intrinsics::maxnumf32(self, other)
899 }
900
901 /// Returns the minimum of the two numbers, ignoring NaN.
902 ///
903 /// If one of the arguments is NaN, then the other argument is returned.
904 /// This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs;
905 /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
906 /// This also matches the behavior of libm’s fmin. In particular, if the inputs compare equal
907 /// (such as for the case of `+0.0` and `-0.0`), either input may be returned non-deterministically.
908 ///
909 /// ```
910 /// let x = 1.0f32;
911 /// let y = 2.0f32;
912 ///
913 /// assert_eq!(x.min(y), x);
914 /// ```
915 #[must_use = "this returns the result of the comparison, without modifying either input"]
916 #[stable(feature = "rust1", since = "1.0.0")]
917 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
918 #[inline]
919 pub const fn min(self, other: f32) -> f32 {
920 intrinsics::minnumf32(self, other)
921 }
922
923 /// Returns the maximum of the two numbers, propagating NaN.
924 ///
925 /// This returns NaN when *either* argument is NaN, as opposed to
926 /// [`f32::max`] which only returns NaN when *both* arguments are NaN.
927 ///
928 /// ```
929 /// #![feature(float_minimum_maximum)]
930 /// let x = 1.0f32;
931 /// let y = 2.0f32;
932 ///
933 /// assert_eq!(x.maximum(y), y);
934 /// assert!(x.maximum(f32::NAN).is_nan());
935 /// ```
936 ///
937 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
938 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
939 /// Note that this follows the semantics specified in IEEE 754-2019.
940 ///
941 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
942 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
943 #[must_use = "this returns the result of the comparison, without modifying either input"]
944 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
945 #[inline]
946 pub const fn maximum(self, other: f32) -> f32 {
947 intrinsics::maximumf32(self, other)
948 }
949
950 /// Returns the minimum of the two numbers, propagating NaN.
951 ///
952 /// This returns NaN when *either* argument is NaN, as opposed to
953 /// [`f32::min`] which only returns NaN when *both* arguments are NaN.
954 ///
955 /// ```
956 /// #![feature(float_minimum_maximum)]
957 /// let x = 1.0f32;
958 /// let y = 2.0f32;
959 ///
960 /// assert_eq!(x.minimum(y), x);
961 /// assert!(x.minimum(f32::NAN).is_nan());
962 /// ```
963 ///
964 /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
965 /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
966 /// Note that this follows the semantics specified in IEEE 754-2019.
967 ///
968 /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
969 /// operand is conserved; see the [specification of NaN bit patterns](f32#nan-bit-patterns) for more info.
970 #[must_use = "this returns the result of the comparison, without modifying either input"]
971 #[unstable(feature = "float_minimum_maximum", issue = "91079")]
972 #[inline]
973 pub const fn minimum(self, other: f32) -> f32 {
974 intrinsics::minimumf32(self, other)
975 }
976
977 /// Calculates the midpoint (average) between `self` and `rhs`.
978 ///
979 /// This returns NaN when *either* argument is NaN or if a combination of
980 /// +inf and -inf is provided as arguments.
981 ///
982 /// # Examples
983 ///
984 /// ```
985 /// assert_eq!(1f32.midpoint(4.0), 2.5);
986 /// assert_eq!((-5.5f32).midpoint(8.0), 1.25);
987 /// ```
988 #[inline]
989 #[doc(alias = "average")]
990 #[stable(feature = "num_midpoint", since = "1.85.0")]
991 #[rustc_const_stable(feature = "num_midpoint", since = "1.85.0")]
992 pub const fn midpoint(self, other: f32) -> f32 {
993 cfg_select! {
994 // Allow faster implementation that have known good 64-bit float
995 // implementations. Falling back to the branchy code on targets that don't
996 // have 64-bit hardware floats or buggy implementations.
997 // https://github.com/rust-lang/rust/pull/121062#issuecomment-2123408114
998 any(
999 target_arch = "x86_64",
1000 target_arch = "aarch64",
1001 all(any(target_arch = "riscv32", target_arch = "riscv64"), target_feature = "d"),
1002 all(target_arch = "loongarch64", target_feature = "d"),
1003 all(target_arch = "arm", target_feature = "vfp2"),
1004 target_arch = "wasm32",
1005 target_arch = "wasm64",
1006 ) => {
1007 ((self as f64 + other as f64) / 2.0) as f32
1008 }
1009 _ => {
1010 const LO: f32 = f32::MIN_POSITIVE * 2.;
1011 const HI: f32 = f32::MAX / 2.;
1012
1013 let (a, b) = (self, other);
1014 let abs_a = a.abs();
1015 let abs_b = b.abs();
1016
1017 if abs_a <= HI && abs_b <= HI {
1018 // Overflow is impossible
1019 (a + b) / 2.
1020 } else if abs_a < LO {
1021 // Not safe to halve `a` (would underflow)
1022 a + (b / 2.)
1023 } else if abs_b < LO {
1024 // Not safe to halve `b` (would underflow)
1025 (a / 2.) + b
1026 } else {
1027 // Safe to halve `a` and `b`
1028 (a / 2.) + (b / 2.)
1029 }
1030 }
1031 }
1032 }
1033
1034 /// Rounds toward zero and converts to any primitive integer type,
1035 /// assuming that the value is finite and fits in that type.
1036 ///
1037 /// ```
1038 /// let value = 4.6_f32;
1039 /// let rounded = unsafe { value.to_int_unchecked::<u16>() };
1040 /// assert_eq!(rounded, 4);
1041 ///
1042 /// let value = -128.9_f32;
1043 /// let rounded = unsafe { value.to_int_unchecked::<i8>() };
1044 /// assert_eq!(rounded, i8::MIN);
1045 /// ```
1046 ///
1047 /// # Safety
1048 ///
1049 /// The value must:
1050 ///
1051 /// * Not be `NaN`
1052 /// * Not be infinite
1053 /// * Be representable in the return type `Int`, after truncating off its fractional part
1054 #[must_use = "this returns the result of the operation, \
1055 without modifying the original"]
1056 #[stable(feature = "float_approx_unchecked_to", since = "1.44.0")]
1057 #[inline]
1058 pub unsafe fn to_int_unchecked<Int>(self) -> Int
1059 where
1060 Self: FloatToInt<Int>,
1061 {
1062 // SAFETY: the caller must uphold the safety contract for
1063 // `FloatToInt::to_int_unchecked`.
1064 unsafe { FloatToInt::<Int>::to_int_unchecked(self) }
1065 }
1066
1067 /// Raw transmutation to `u32`.
1068 ///
1069 /// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
1070 ///
1071 /// See [`from_bits`](Self::from_bits) for some discussion of the
1072 /// portability of this operation (there are almost no issues).
1073 ///
1074 /// Note that this function is distinct from `as` casting, which attempts to
1075 /// preserve the *numeric* value, and not the bitwise value.
1076 ///
1077 /// # Examples
1078 ///
1079 /// ```
1080 /// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
1081 /// assert_eq!((12.5f32).to_bits(), 0x41480000);
1082 ///
1083 /// ```
1084 #[must_use = "this returns the result of the operation, \
1085 without modifying the original"]
1086 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1087 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1088 #[inline]
1089 #[allow(unnecessary_transmutes)]
1090 pub const fn to_bits(self) -> u32 {
1091 // SAFETY: `u32` is a plain old datatype so we can always transmute to it.
1092 unsafe { mem::transmute(self) }
1093 }
1094
1095 /// Raw transmutation from `u32`.
1096 ///
1097 /// This is currently identical to `transmute::<u32, f32>(v)` on all platforms.
1098 /// It turns out this is incredibly portable, for two reasons:
1099 ///
1100 /// * Floats and Ints have the same endianness on all supported platforms.
1101 /// * IEEE 754 very precisely specifies the bit layout of floats.
1102 ///
1103 /// However there is one caveat: prior to the 2008 version of IEEE 754, how
1104 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
1105 /// (notably x86 and ARM) picked the interpretation that was ultimately
1106 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
1107 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
1108 ///
1109 /// Rather than trying to preserve signaling-ness cross-platform, this
1110 /// implementation favors preserving the exact bits. This means that
1111 /// any payloads encoded in NaNs will be preserved even if the result of
1112 /// this method is sent over the network from an x86 machine to a MIPS one.
1113 ///
1114 /// If the results of this method are only manipulated by the same
1115 /// architecture that produced them, then there is no portability concern.
1116 ///
1117 /// If the input isn't NaN, then there is no portability concern.
1118 ///
1119 /// If you don't care about signalingness (very likely), then there is no
1120 /// portability concern.
1121 ///
1122 /// Note that this function is distinct from `as` casting, which attempts to
1123 /// preserve the *numeric* value, and not the bitwise value.
1124 ///
1125 /// # Examples
1126 ///
1127 /// ```
1128 /// let v = f32::from_bits(0x41480000);
1129 /// assert_eq!(v, 12.5);
1130 /// ```
1131 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1132 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1133 #[must_use]
1134 #[inline]
1135 #[allow(unnecessary_transmutes)]
1136 pub const fn from_bits(v: u32) -> Self {
1137 // It turns out the safety issues with sNaN were overblown! Hooray!
1138 // SAFETY: `u32` is a plain old datatype so we can always transmute from it.
1139 unsafe { mem::transmute(v) }
1140 }
1141
1142 /// Returns the memory representation of this floating point number as a byte array in
1143 /// big-endian (network) byte order.
1144 ///
1145 /// See [`from_bits`](Self::from_bits) for some discussion of the
1146 /// portability of this operation (there are almost no issues).
1147 ///
1148 /// # Examples
1149 ///
1150 /// ```
1151 /// let bytes = 12.5f32.to_be_bytes();
1152 /// assert_eq!(bytes, [0x41, 0x48, 0x00, 0x00]);
1153 /// ```
1154 #[must_use = "this returns the result of the operation, \
1155 without modifying the original"]
1156 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1157 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1158 #[inline]
1159 pub const fn to_be_bytes(self) -> [u8; 4] {
1160 self.to_bits().to_be_bytes()
1161 }
1162
1163 /// Returns the memory representation of this floating point number as a byte array in
1164 /// little-endian byte order.
1165 ///
1166 /// See [`from_bits`](Self::from_bits) for some discussion of the
1167 /// portability of this operation (there are almost no issues).
1168 ///
1169 /// # Examples
1170 ///
1171 /// ```
1172 /// let bytes = 12.5f32.to_le_bytes();
1173 /// assert_eq!(bytes, [0x00, 0x00, 0x48, 0x41]);
1174 /// ```
1175 #[must_use = "this returns the result of the operation, \
1176 without modifying the original"]
1177 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1178 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1179 #[inline]
1180 pub const fn to_le_bytes(self) -> [u8; 4] {
1181 self.to_bits().to_le_bytes()
1182 }
1183
1184 /// Returns the memory representation of this floating point number as a byte array in
1185 /// native byte order.
1186 ///
1187 /// As the target platform's native endianness is used, portable code
1188 /// should use [`to_be_bytes`] or [`to_le_bytes`], as appropriate, instead.
1189 ///
1190 /// [`to_be_bytes`]: f32::to_be_bytes
1191 /// [`to_le_bytes`]: f32::to_le_bytes
1192 ///
1193 /// See [`from_bits`](Self::from_bits) for some discussion of the
1194 /// portability of this operation (there are almost no issues).
1195 ///
1196 /// # Examples
1197 ///
1198 /// ```
1199 /// let bytes = 12.5f32.to_ne_bytes();
1200 /// assert_eq!(
1201 /// bytes,
1202 /// if cfg!(target_endian = "big") {
1203 /// [0x41, 0x48, 0x00, 0x00]
1204 /// } else {
1205 /// [0x00, 0x00, 0x48, 0x41]
1206 /// }
1207 /// );
1208 /// ```
1209 #[must_use = "this returns the result of the operation, \
1210 without modifying the original"]
1211 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1212 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1213 #[inline]
1214 pub const fn to_ne_bytes(self) -> [u8; 4] {
1215 self.to_bits().to_ne_bytes()
1216 }
1217
1218 /// Creates a floating point value from its representation as a byte array in big endian.
1219 ///
1220 /// See [`from_bits`](Self::from_bits) for some discussion of the
1221 /// portability of this operation (there are almost no issues).
1222 ///
1223 /// # Examples
1224 ///
1225 /// ```
1226 /// let value = f32::from_be_bytes([0x41, 0x48, 0x00, 0x00]);
1227 /// assert_eq!(value, 12.5);
1228 /// ```
1229 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1230 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1231 #[must_use]
1232 #[inline]
1233 pub const fn from_be_bytes(bytes: [u8; 4]) -> Self {
1234 Self::from_bits(u32::from_be_bytes(bytes))
1235 }
1236
1237 /// Creates a floating point value from its representation as a byte array in little endian.
1238 ///
1239 /// See [`from_bits`](Self::from_bits) for some discussion of the
1240 /// portability of this operation (there are almost no issues).
1241 ///
1242 /// # Examples
1243 ///
1244 /// ```
1245 /// let value = f32::from_le_bytes([0x00, 0x00, 0x48, 0x41]);
1246 /// assert_eq!(value, 12.5);
1247 /// ```
1248 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1249 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1250 #[must_use]
1251 #[inline]
1252 pub const fn from_le_bytes(bytes: [u8; 4]) -> Self {
1253 Self::from_bits(u32::from_le_bytes(bytes))
1254 }
1255
1256 /// Creates a floating point value from its representation as a byte array in native endian.
1257 ///
1258 /// As the target platform's native endianness is used, portable code
1259 /// likely wants to use [`from_be_bytes`] or [`from_le_bytes`], as
1260 /// appropriate instead.
1261 ///
1262 /// [`from_be_bytes`]: f32::from_be_bytes
1263 /// [`from_le_bytes`]: f32::from_le_bytes
1264 ///
1265 /// See [`from_bits`](Self::from_bits) for some discussion of the
1266 /// portability of this operation (there are almost no issues).
1267 ///
1268 /// # Examples
1269 ///
1270 /// ```
1271 /// let value = f32::from_ne_bytes(if cfg!(target_endian = "big") {
1272 /// [0x41, 0x48, 0x00, 0x00]
1273 /// } else {
1274 /// [0x00, 0x00, 0x48, 0x41]
1275 /// });
1276 /// assert_eq!(value, 12.5);
1277 /// ```
1278 #[stable(feature = "float_to_from_bytes", since = "1.40.0")]
1279 #[rustc_const_stable(feature = "const_float_bits_conv", since = "1.83.0")]
1280 #[must_use]
1281 #[inline]
1282 pub const fn from_ne_bytes(bytes: [u8; 4]) -> Self {
1283 Self::from_bits(u32::from_ne_bytes(bytes))
1284 }
1285
1286 /// Returns the ordering between `self` and `other`.
1287 ///
1288 /// Unlike the standard partial comparison between floating point numbers,
1289 /// this comparison always produces an ordering in accordance to
1290 /// the `totalOrder` predicate as defined in the IEEE 754 (2008 revision)
1291 /// floating point standard. The values are ordered in the following sequence:
1292 ///
1293 /// - negative quiet NaN
1294 /// - negative signaling NaN
1295 /// - negative infinity
1296 /// - negative numbers
1297 /// - negative subnormal numbers
1298 /// - negative zero
1299 /// - positive zero
1300 /// - positive subnormal numbers
1301 /// - positive numbers
1302 /// - positive infinity
1303 /// - positive signaling NaN
1304 /// - positive quiet NaN.
1305 ///
1306 /// The ordering established by this function does not always agree with the
1307 /// [`PartialOrd`] and [`PartialEq`] implementations of `f32`. For example,
1308 /// they consider negative and positive zero equal, while `total_cmp`
1309 /// doesn't.
1310 ///
1311 /// The interpretation of the signaling NaN bit follows the definition in
1312 /// the IEEE 754 standard, which may not match the interpretation by some of
1313 /// the older, non-conformant (e.g. MIPS) hardware implementations.
1314 ///
1315 /// # Example
1316 ///
1317 /// ```
1318 /// struct GoodBoy {
1319 /// name: String,
1320 /// weight: f32,
1321 /// }
1322 ///
1323 /// let mut bois = vec![
1324 /// GoodBoy { name: "Pucci".to_owned(), weight: 0.1 },
1325 /// GoodBoy { name: "Woofer".to_owned(), weight: 99.0 },
1326 /// GoodBoy { name: "Yapper".to_owned(), weight: 10.0 },
1327 /// GoodBoy { name: "Chonk".to_owned(), weight: f32::INFINITY },
1328 /// GoodBoy { name: "Abs. Unit".to_owned(), weight: f32::NAN },
1329 /// GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
1330 /// ];
1331 ///
1332 /// bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));
1333 ///
1334 /// // `f32::NAN` could be positive or negative, which will affect the sort order.
1335 /// if f32::NAN.is_sign_negative() {
1336 /// assert!(bois.into_iter().map(|b| b.weight)
1337 /// .zip([f32::NAN, -5.0, 0.1, 10.0, 99.0, f32::INFINITY].iter())
1338 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1339 /// } else {
1340 /// assert!(bois.into_iter().map(|b| b.weight)
1341 /// .zip([-5.0, 0.1, 10.0, 99.0, f32::INFINITY, f32::NAN].iter())
1342 /// .all(|(a, b)| a.to_bits() == b.to_bits()))
1343 /// }
1344 /// ```
1345 #[stable(feature = "total_cmp", since = "1.62.0")]
1346 #[must_use]
1347 #[inline]
1348 pub fn total_cmp(&self, other: &Self) -> crate::cmp::Ordering {
1349 let mut left = self.to_bits() as i32;
1350 let mut right = other.to_bits() as i32;
1351
1352 // In case of negatives, flip all the bits except the sign
1353 // to achieve a similar layout as two's complement integers
1354 //
1355 // Why does this work? IEEE 754 floats consist of three fields:
1356 // Sign bit, exponent and mantissa. The set of exponent and mantissa
1357 // fields as a whole have the property that their bitwise order is
1358 // equal to the numeric magnitude where the magnitude is defined.
1359 // The magnitude is not normally defined on NaN values, but
1360 // IEEE 754 totalOrder defines the NaN values also to follow the
1361 // bitwise order. This leads to order explained in the doc comment.
1362 // However, the representation of magnitude is the same for negative
1363 // and positive numbers – only the sign bit is different.
1364 // To easily compare the floats as signed integers, we need to
1365 // flip the exponent and mantissa bits in case of negative numbers.
1366 // We effectively convert the numbers to "two's complement" form.
1367 //
1368 // To do the flipping, we construct a mask and XOR against it.
1369 // We branchlessly calculate an "all-ones except for the sign bit"
1370 // mask from negative-signed values: right shifting sign-extends
1371 // the integer, so we "fill" the mask with sign bits, and then
1372 // convert to unsigned to push one more zero bit.
1373 // On positive values, the mask is all zeros, so it's a no-op.
1374 left ^= (((left >> 31) as u32) >> 1) as i32;
1375 right ^= (((right >> 31) as u32) >> 1) as i32;
1376
1377 left.cmp(&right)
1378 }
1379
1380 /// Restrict a value to a certain interval unless it is NaN.
1381 ///
1382 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
1383 /// less than `min`. Otherwise this returns `self`.
1384 ///
1385 /// Note that this function returns NaN if the initial value was NaN as
1386 /// well.
1387 ///
1388 /// # Panics
1389 ///
1390 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
1391 ///
1392 /// # Examples
1393 ///
1394 /// ```
1395 /// assert!((-3.0f32).clamp(-2.0, 1.0) == -2.0);
1396 /// assert!((0.0f32).clamp(-2.0, 1.0) == 0.0);
1397 /// assert!((2.0f32).clamp(-2.0, 1.0) == 1.0);
1398 /// assert!((f32::NAN).clamp(-2.0, 1.0).is_nan());
1399 /// ```
1400 #[must_use = "method returns a new number and does not mutate the original value"]
1401 #[stable(feature = "clamp", since = "1.50.0")]
1402 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1403 #[inline]
1404 pub const fn clamp(mut self, min: f32, max: f32) -> f32 {
1405 const_assert!(
1406 min <= max,
1407 "min > max, or either was NaN",
1408 "min > max, or either was NaN. min = {min:?}, max = {max:?}",
1409 min: f32,
1410 max: f32,
1411 );
1412
1413 if self < min {
1414 self = min;
1415 }
1416 if self > max {
1417 self = max;
1418 }
1419 self
1420 }
1421
1422 /// Computes the absolute value of `self`.
1423 ///
1424 /// This function always returns the precise result.
1425 ///
1426 /// # Examples
1427 ///
1428 /// ```
1429 /// let x = 3.5_f32;
1430 /// let y = -3.5_f32;
1431 ///
1432 /// assert_eq!(x.abs(), x);
1433 /// assert_eq!(y.abs(), -y);
1434 ///
1435 /// assert!(f32::NAN.abs().is_nan());
1436 /// ```
1437 #[must_use = "method returns a new number and does not mutate the original value"]
1438 #[stable(feature = "rust1", since = "1.0.0")]
1439 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1440 #[inline]
1441 pub const fn abs(self) -> f32 {
1442 // SAFETY: this is actually a safe intrinsic
1443 unsafe { intrinsics::fabsf32(self) }
1444 }
1445
1446 /// Returns a number that represents the sign of `self`.
1447 ///
1448 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
1449 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
1450 /// - NaN if the number is NaN
1451 ///
1452 /// # Examples
1453 ///
1454 /// ```
1455 /// let f = 3.5_f32;
1456 ///
1457 /// assert_eq!(f.signum(), 1.0);
1458 /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
1459 ///
1460 /// assert!(f32::NAN.signum().is_nan());
1461 /// ```
1462 #[must_use = "method returns a new number and does not mutate the original value"]
1463 #[stable(feature = "rust1", since = "1.0.0")]
1464 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1465 #[inline]
1466 pub const fn signum(self) -> f32 {
1467 if self.is_nan() { Self::NAN } else { 1.0_f32.copysign(self) }
1468 }
1469
1470 /// Returns a number composed of the magnitude of `self` and the sign of
1471 /// `sign`.
1472 ///
1473 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise equal to `-self`.
1474 /// If `self` is a NaN, then a NaN with the same payload as `self` and the sign bit of `sign` is
1475 /// returned.
1476 ///
1477 /// If `sign` is a NaN, then this operation will still carry over its sign into the result. Note
1478 /// that IEEE 754 doesn't assign any meaning to the sign bit in case of a NaN, and as Rust
1479 /// doesn't guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the
1480 /// result of `copysign` with `sign` being a NaN might produce an unexpected or non-portable
1481 /// result. See the [specification of NaN bit patterns](primitive@f32#nan-bit-patterns) for more
1482 /// info.
1483 ///
1484 /// # Examples
1485 ///
1486 /// ```
1487 /// let f = 3.5_f32;
1488 ///
1489 /// assert_eq!(f.copysign(0.42), 3.5_f32);
1490 /// assert_eq!(f.copysign(-0.42), -3.5_f32);
1491 /// assert_eq!((-f).copysign(0.42), 3.5_f32);
1492 /// assert_eq!((-f).copysign(-0.42), -3.5_f32);
1493 ///
1494 /// assert!(f32::NAN.copysign(1.0).is_nan());
1495 /// ```
1496 #[must_use = "method returns a new number and does not mutate the original value"]
1497 #[inline]
1498 #[stable(feature = "copysign", since = "1.35.0")]
1499 #[rustc_const_stable(feature = "const_float_methods", since = "1.85.0")]
1500 pub const fn copysign(self, sign: f32) -> f32 {
1501 // SAFETY: this is actually a safe intrinsic
1502 unsafe { intrinsics::copysignf32(self, sign) }
1503 }
1504
1505 /// Float addition that allows optimizations based on algebraic rules.
1506 ///
1507 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1508 #[must_use = "method returns a new number and does not mutate the original value"]
1509 #[unstable(feature = "float_algebraic", issue = "136469")]
1510 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1511 #[inline]
1512 pub const fn algebraic_add(self, rhs: f32) -> f32 {
1513 intrinsics::fadd_algebraic(self, rhs)
1514 }
1515
1516 /// Float subtraction that allows optimizations based on algebraic rules.
1517 ///
1518 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1519 #[must_use = "method returns a new number and does not mutate the original value"]
1520 #[unstable(feature = "float_algebraic", issue = "136469")]
1521 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1522 #[inline]
1523 pub const fn algebraic_sub(self, rhs: f32) -> f32 {
1524 intrinsics::fsub_algebraic(self, rhs)
1525 }
1526
1527 /// Float multiplication that allows optimizations based on algebraic rules.
1528 ///
1529 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1530 #[must_use = "method returns a new number and does not mutate the original value"]
1531 #[unstable(feature = "float_algebraic", issue = "136469")]
1532 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1533 #[inline]
1534 pub const fn algebraic_mul(self, rhs: f32) -> f32 {
1535 intrinsics::fmul_algebraic(self, rhs)
1536 }
1537
1538 /// Float division that allows optimizations based on algebraic rules.
1539 ///
1540 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1541 #[must_use = "method returns a new number and does not mutate the original value"]
1542 #[unstable(feature = "float_algebraic", issue = "136469")]
1543 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1544 #[inline]
1545 pub const fn algebraic_div(self, rhs: f32) -> f32 {
1546 intrinsics::fdiv_algebraic(self, rhs)
1547 }
1548
1549 /// Float remainder that allows optimizations based on algebraic rules.
1550 ///
1551 /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
1552 #[must_use = "method returns a new number and does not mutate the original value"]
1553 #[unstable(feature = "float_algebraic", issue = "136469")]
1554 #[rustc_const_unstable(feature = "float_algebraic", issue = "136469")]
1555 #[inline]
1556 pub const fn algebraic_rem(self, rhs: f32) -> f32 {
1557 intrinsics::frem_algebraic(self, rhs)
1558 }
1559}
1560
1561/// Experimental implementations of floating point functions in `core`.
1562///
1563/// _The standalone functions in this module are for testing only.
1564/// They will be stabilized as inherent methods._
1565#[unstable(feature = "core_float_math", issue = "137578")]
1566pub mod math {
1567 use crate::intrinsics;
1568 use crate::num::libm;
1569
1570 /// Experimental version of `floor` in `core`. See [`f32::floor`] for details.
1571 ///
1572 /// # Examples
1573 ///
1574 /// ```
1575 /// #![feature(core_float_math)]
1576 ///
1577 /// use core::f32;
1578 ///
1579 /// let f = 3.7_f32;
1580 /// let g = 3.0_f32;
1581 /// let h = -3.7_f32;
1582 ///
1583 /// assert_eq!(f32::math::floor(f), 3.0);
1584 /// assert_eq!(f32::math::floor(g), 3.0);
1585 /// assert_eq!(f32::math::floor(h), -4.0);
1586 /// ```
1587 ///
1588 /// _This standalone function is for testing only.
1589 /// It will be stabilized as an inherent method._
1590 ///
1591 /// [`f32::floor`]: ../../../std/primitive.f32.html#method.floor
1592 #[inline]
1593 #[unstable(feature = "core_float_math", issue = "137578")]
1594 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1595 #[must_use = "method returns a new number and does not mutate the original value"]
1596 pub const fn floor(x: f32) -> f32 {
1597 // SAFETY: intrinsic with no preconditions
1598 unsafe { intrinsics::floorf32(x) }
1599 }
1600
1601 /// Experimental version of `ceil` in `core`. See [`f32::ceil`] for details.
1602 ///
1603 /// # Examples
1604 ///
1605 /// ```
1606 /// #![feature(core_float_math)]
1607 ///
1608 /// use core::f32;
1609 ///
1610 /// let f = 3.01_f32;
1611 /// let g = 4.0_f32;
1612 ///
1613 /// assert_eq!(f32::math::ceil(f), 4.0);
1614 /// assert_eq!(f32::math::ceil(g), 4.0);
1615 /// ```
1616 ///
1617 /// _This standalone function is for testing only.
1618 /// It will be stabilized as an inherent method._
1619 ///
1620 /// [`f32::ceil`]: ../../../std/primitive.f32.html#method.ceil
1621 #[inline]
1622 #[doc(alias = "ceiling")]
1623 #[must_use = "method returns a new number and does not mutate the original value"]
1624 #[unstable(feature = "core_float_math", issue = "137578")]
1625 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1626 pub const fn ceil(x: f32) -> f32 {
1627 // SAFETY: intrinsic with no preconditions
1628 unsafe { intrinsics::ceilf32(x) }
1629 }
1630
1631 /// Experimental version of `round` in `core`. See [`f32::round`] for details.
1632 ///
1633 /// # Examples
1634 ///
1635 /// ```
1636 /// #![feature(core_float_math)]
1637 ///
1638 /// use core::f32;
1639 ///
1640 /// let f = 3.3_f32;
1641 /// let g = -3.3_f32;
1642 /// let h = -3.7_f32;
1643 /// let i = 3.5_f32;
1644 /// let j = 4.5_f32;
1645 ///
1646 /// assert_eq!(f32::math::round(f), 3.0);
1647 /// assert_eq!(f32::math::round(g), -3.0);
1648 /// assert_eq!(f32::math::round(h), -4.0);
1649 /// assert_eq!(f32::math::round(i), 4.0);
1650 /// assert_eq!(f32::math::round(j), 5.0);
1651 /// ```
1652 ///
1653 /// _This standalone function is for testing only.
1654 /// It will be stabilized as an inherent method._
1655 ///
1656 /// [`f32::round`]: ../../../std/primitive.f32.html#method.round
1657 #[inline]
1658 #[unstable(feature = "core_float_math", issue = "137578")]
1659 #[must_use = "method returns a new number and does not mutate the original value"]
1660 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1661 pub const fn round(x: f32) -> f32 {
1662 // SAFETY: intrinsic with no preconditions
1663 unsafe { intrinsics::roundf32(x) }
1664 }
1665
1666 /// Experimental version of `round_ties_even` in `core`. See [`f32::round_ties_even`] for
1667 /// details.
1668 ///
1669 /// # Examples
1670 ///
1671 /// ```
1672 /// #![feature(core_float_math)]
1673 ///
1674 /// use core::f32;
1675 ///
1676 /// let f = 3.3_f32;
1677 /// let g = -3.3_f32;
1678 /// let h = 3.5_f32;
1679 /// let i = 4.5_f32;
1680 ///
1681 /// assert_eq!(f32::math::round_ties_even(f), 3.0);
1682 /// assert_eq!(f32::math::round_ties_even(g), -3.0);
1683 /// assert_eq!(f32::math::round_ties_even(h), 4.0);
1684 /// assert_eq!(f32::math::round_ties_even(i), 4.0);
1685 /// ```
1686 ///
1687 /// _This standalone function is for testing only.
1688 /// It will be stabilized as an inherent method._
1689 ///
1690 /// [`f32::round_ties_even`]: ../../../std/primitive.f32.html#method.round_ties_even
1691 #[inline]
1692 #[unstable(feature = "core_float_math", issue = "137578")]
1693 #[must_use = "method returns a new number and does not mutate the original value"]
1694 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1695 pub const fn round_ties_even(x: f32) -> f32 {
1696 intrinsics::round_ties_even_f32(x)
1697 }
1698
1699 /// Experimental version of `trunc` in `core`. See [`f32::trunc`] for details.
1700 ///
1701 /// # Examples
1702 ///
1703 /// ```
1704 /// #![feature(core_float_math)]
1705 ///
1706 /// use core::f32;
1707 ///
1708 /// let f = 3.7_f32;
1709 /// let g = 3.0_f32;
1710 /// let h = -3.7_f32;
1711 ///
1712 /// assert_eq!(f32::math::trunc(f), 3.0);
1713 /// assert_eq!(f32::math::trunc(g), 3.0);
1714 /// assert_eq!(f32::math::trunc(h), -3.0);
1715 /// ```
1716 ///
1717 /// _This standalone function is for testing only.
1718 /// It will be stabilized as an inherent method._
1719 ///
1720 /// [`f32::trunc`]: ../../../std/primitive.f32.html#method.trunc
1721 #[inline]
1722 #[doc(alias = "truncate")]
1723 #[must_use = "method returns a new number and does not mutate the original value"]
1724 #[unstable(feature = "core_float_math", issue = "137578")]
1725 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1726 pub const fn trunc(x: f32) -> f32 {
1727 // SAFETY: intrinsic with no preconditions
1728 unsafe { intrinsics::truncf32(x) }
1729 }
1730
1731 /// Experimental version of `fract` in `core`. See [`f32::fract`] for details.
1732 ///
1733 /// # Examples
1734 ///
1735 /// ```
1736 /// #![feature(core_float_math)]
1737 ///
1738 /// use core::f32;
1739 ///
1740 /// let x = 3.6_f32;
1741 /// let y = -3.6_f32;
1742 /// let abs_difference_x = (f32::math::fract(x) - 0.6).abs();
1743 /// let abs_difference_y = (f32::math::fract(y) - (-0.6)).abs();
1744 ///
1745 /// assert!(abs_difference_x <= f32::EPSILON);
1746 /// assert!(abs_difference_y <= f32::EPSILON);
1747 /// ```
1748 ///
1749 /// _This standalone function is for testing only.
1750 /// It will be stabilized as an inherent method._
1751 ///
1752 /// [`f32::fract`]: ../../../std/primitive.f32.html#method.fract
1753 #[inline]
1754 #[unstable(feature = "core_float_math", issue = "137578")]
1755 #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
1756 #[must_use = "method returns a new number and does not mutate the original value"]
1757 pub const fn fract(x: f32) -> f32 {
1758 x - trunc(x)
1759 }
1760
1761 /// Experimental version of `mul_add` in `core`. See [`f32::mul_add`] for details.
1762 ///
1763 /// # Examples
1764 ///
1765 /// ```
1766 /// #![feature(core_float_math)]
1767 ///
1768 /// # // FIXME(#140515): mingw has an incorrect fma
1769 /// # // https://sourceforge.net/p/mingw-w64/bugs/848/
1770 /// # #[cfg(all(target_os = "windows", target_env = "gnu", not(target_abi = "llvm")))] {
1771 /// use core::f32;
1772 ///
1773 /// let m = 10.0_f32;
1774 /// let x = 4.0_f32;
1775 /// let b = 60.0_f32;
1776 ///
1777 /// assert_eq!(f32::math::mul_add(m, x, b), 100.0);
1778 /// assert_eq!(m * x + b, 100.0);
1779 ///
1780 /// let one_plus_eps = 1.0_f32 + f32::EPSILON;
1781 /// let one_minus_eps = 1.0_f32 - f32::EPSILON;
1782 /// let minus_one = -1.0_f32;
1783 ///
1784 /// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.
1785 /// assert_eq!(
1786 /// f32::math::mul_add(one_plus_eps, one_minus_eps, minus_one),
1787 /// -f32::EPSILON * f32::EPSILON
1788 /// );
1789 /// // Different rounding with the non-fused multiply and add.
1790 /// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0);
1791 /// # }
1792 /// ```
1793 ///
1794 /// _This standalone function is for testing only.
1795 /// It will be stabilized as an inherent method._
1796 ///
1797 /// [`f32::mul_add`]: ../../../std/primitive.f32.html#method.mul_add
1798 #[inline]
1799 #[doc(alias = "fmaf", alias = "fusedMultiplyAdd")]
1800 #[must_use = "method returns a new number and does not mutate the original value"]
1801 #[unstable(feature = "core_float_math", issue = "137578")]
1802 pub fn mul_add(x: f32, y: f32, z: f32) -> f32 {
1803 // SAFETY: intrinsic with no preconditions
1804 unsafe { intrinsics::fmaf32(x, y, z) }
1805 }
1806
1807 /// Experimental version of `div_euclid` in `core`. See [`f32::div_euclid`] for details.
1808 ///
1809 /// # Examples
1810 ///
1811 /// ```
1812 /// #![feature(core_float_math)]
1813 ///
1814 /// use core::f32;
1815 ///
1816 /// let a: f32 = 7.0;
1817 /// let b = 4.0;
1818 /// assert_eq!(f32::math::div_euclid(a, b), 1.0); // 7.0 > 4.0 * 1.0
1819 /// assert_eq!(f32::math::div_euclid(-a, b), -2.0); // -7.0 >= 4.0 * -2.0
1820 /// assert_eq!(f32::math::div_euclid(a, -b), -1.0); // 7.0 >= -4.0 * -1.0
1821 /// assert_eq!(f32::math::div_euclid(-a, -b), 2.0); // -7.0 >= -4.0 * 2.0
1822 /// ```
1823 ///
1824 /// _This standalone function is for testing only.
1825 /// It will be stabilized as an inherent method._
1826 ///
1827 /// [`f32::div_euclid`]: ../../../std/primitive.f32.html#method.div_euclid
1828 #[inline]
1829 #[unstable(feature = "core_float_math", issue = "137578")]
1830 #[must_use = "method returns a new number and does not mutate the original value"]
1831 pub fn div_euclid(x: f32, rhs: f32) -> f32 {
1832 let q = trunc(x / rhs);
1833 if x % rhs < 0.0 {
1834 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
1835 }
1836 q
1837 }
1838
1839 /// Experimental version of `rem_euclid` in `core`. See [`f32::rem_euclid`] for details.
1840 ///
1841 /// # Examples
1842 ///
1843 /// ```
1844 /// #![feature(core_float_math)]
1845 ///
1846 /// use core::f32;
1847 ///
1848 /// let a: f32 = 7.0;
1849 /// let b = 4.0;
1850 /// assert_eq!(f32::math::rem_euclid(a, b), 3.0);
1851 /// assert_eq!(f32::math::rem_euclid(-a, b), 1.0);
1852 /// assert_eq!(f32::math::rem_euclid(a, -b), 3.0);
1853 /// assert_eq!(f32::math::rem_euclid(-a, -b), 1.0);
1854 /// // limitation due to round-off error
1855 /// assert!(f32::math::rem_euclid(-f32::EPSILON, 3.0) != 0.0);
1856 /// ```
1857 ///
1858 /// _This standalone function is for testing only.
1859 /// It will be stabilized as an inherent method._
1860 ///
1861 /// [`f32::rem_euclid`]: ../../../std/primitive.f32.html#method.rem_euclid
1862 #[inline]
1863 #[doc(alias = "modulo", alias = "mod")]
1864 #[unstable(feature = "core_float_math", issue = "137578")]
1865 #[must_use = "method returns a new number and does not mutate the original value"]
1866 pub fn rem_euclid(x: f32, rhs: f32) -> f32 {
1867 let r = x % rhs;
1868 if r < 0.0 { r + rhs.abs() } else { r }
1869 }
1870
1871 /// Experimental version of `powi` in `core`. See [`f32::powi`] for details.
1872 ///
1873 /// # Examples
1874 ///
1875 /// ```
1876 /// #![feature(core_float_math)]
1877 ///
1878 /// use core::f32;
1879 ///
1880 /// let x = 2.0_f32;
1881 /// let abs_difference = (f32::math::powi(x, 2) - (x * x)).abs();
1882 /// assert!(abs_difference <= 1e-5);
1883 ///
1884 /// assert_eq!(f32::math::powi(f32::NAN, 0), 1.0);
1885 /// ```
1886 ///
1887 /// _This standalone function is for testing only.
1888 /// It will be stabilized as an inherent method._
1889 ///
1890 /// [`f32::powi`]: ../../../std/primitive.f32.html#method.powi
1891 #[inline]
1892 #[must_use = "method returns a new number and does not mutate the original value"]
1893 #[unstable(feature = "core_float_math", issue = "137578")]
1894 pub fn powi(x: f32, n: i32) -> f32 {
1895 // SAFETY: intrinsic with no preconditions
1896 unsafe { intrinsics::powif32(x, n) }
1897 }
1898
1899 /// Experimental version of `sqrt` in `core`. See [`f32::sqrt`] for details.
1900 ///
1901 /// # Examples
1902 ///
1903 /// ```
1904 /// #![feature(core_float_math)]
1905 ///
1906 /// use core::f32;
1907 ///
1908 /// let positive = 4.0_f32;
1909 /// let negative = -4.0_f32;
1910 /// let negative_zero = -0.0_f32;
1911 ///
1912 /// assert_eq!(f32::math::sqrt(positive), 2.0);
1913 /// assert!(f32::math::sqrt(negative).is_nan());
1914 /// assert_eq!(f32::math::sqrt(negative_zero), negative_zero);
1915 /// ```
1916 ///
1917 /// _This standalone function is for testing only.
1918 /// It will be stabilized as an inherent method._
1919 ///
1920 /// [`f32::sqrt`]: ../../../std/primitive.f32.html#method.sqrt
1921 #[inline]
1922 #[doc(alias = "squareRoot")]
1923 #[unstable(feature = "core_float_math", issue = "137578")]
1924 #[must_use = "method returns a new number and does not mutate the original value"]
1925 pub fn sqrt(x: f32) -> f32 {
1926 // SAFETY: intrinsic with no preconditions
1927 unsafe { intrinsics::sqrtf32(x) }
1928 }
1929
1930 /// Experimental version of `abs_sub` in `core`. See [`f32::abs_sub`] for details.
1931 ///
1932 /// # Examples
1933 ///
1934 /// ```
1935 /// #![feature(core_float_math)]
1936 ///
1937 /// use core::f32;
1938 ///
1939 /// let x = 3.0f32;
1940 /// let y = -3.0f32;
1941 ///
1942 /// let abs_difference_x = (f32::math::abs_sub(x, 1.0) - 2.0).abs();
1943 /// let abs_difference_y = (f32::math::abs_sub(y, 1.0) - 0.0).abs();
1944 ///
1945 /// assert!(abs_difference_x <= f32::EPSILON);
1946 /// assert!(abs_difference_y <= f32::EPSILON);
1947 /// ```
1948 ///
1949 /// _This standalone function is for testing only.
1950 /// It will be stabilized as an inherent method._
1951 ///
1952 /// [`f32::abs_sub`]: ../../../std/primitive.f32.html#method.abs_sub
1953 #[inline]
1954 #[stable(feature = "rust1", since = "1.0.0")]
1955 #[deprecated(
1956 since = "1.10.0",
1957 note = "you probably meant `(self - other).abs()`: \
1958 this operation is `(self - other).max(0.0)` \
1959 except that `abs_sub` also propagates NaNs (also \
1960 known as `fdimf` in C). If you truly need the positive \
1961 difference, consider using that expression or the C function \
1962 `fdimf`, depending on how you wish to handle NaN (please consider \
1963 filing an issue describing your use-case too)."
1964 )]
1965 #[must_use = "method returns a new number and does not mutate the original value"]
1966 pub fn abs_sub(x: f32, other: f32) -> f32 {
1967 libm::fdimf(x, other)
1968 }
1969
1970 /// Experimental version of `cbrt` in `core`. See [`f32::cbrt`] for details.
1971 ///
1972 /// # Unspecified precision
1973 ///
1974 /// The precision of this function is non-deterministic. This means it varies by platform, Rust version, and
1975 /// can even differ within the same execution from one invocation to the next.
1976 /// This function currently corresponds to the `cbrtf` from libc on Unix
1977 /// and Windows. Note that this might change in the future.
1978 ///
1979 /// # Examples
1980 ///
1981 /// ```
1982 /// #![feature(core_float_math)]
1983 ///
1984 /// use core::f32;
1985 ///
1986 /// let x = 8.0f32;
1987 ///
1988 /// // x^(1/3) - 2 == 0
1989 /// let abs_difference = (f32::math::cbrt(x) - 2.0).abs();
1990 ///
1991 /// assert!(abs_difference <= f32::EPSILON);
1992 /// ```
1993 ///
1994 /// _This standalone function is for testing only.
1995 /// It will be stabilized as an inherent method._
1996 ///
1997 /// [`f32::cbrt`]: ../../../std/primitive.f32.html#method.cbrt
1998 #[inline]
1999 #[must_use = "method returns a new number and does not mutate the original value"]
2000 #[unstable(feature = "core_float_math", issue = "137578")]
2001 pub fn cbrt(x: f32) -> f32 {
2002 libm::cbrtf(x)
2003 }
2004}
2005